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Abstract:
The Electromagnetic (EM) fields excited by a vertical electric dipole (VED) at the ultra-low frequency (ULF) have been widely used in different studies such as space weather, earthquake predictions, geophysical investigations, and communications. Algorithms are essential for estimations of worldwide EM fields. Spherical coordinates are widely used in these studies as the curvature of the earth cannot be ignored. The ULF EM fields are usually expressed by series of spherical harmonics, including spherical Bessel and Hankel functions. There are overflow problem when separately estimating values of spherical harmonics and divergence problem when evaluating summation of series expression of ULF EM fields. This study proposes a new algorithm to calculate EM fields excited by a VED embedded in a layered spherical model. The ULF EM fields are expressed by normalized spherical Bessel/Hankel functions, where a set of local/general reflection and transmission coefficients is defined to describe propagations of EM fields in each spherical layer. The normalized spherical Bessel/Hankel functions are not only useful to overcome the overflow problem in calculations of spherical Bessel/Hankel functions but also helpful to accelerate the convergence of calculations EM fields as the normalized expressions mitigate small oscillations terms. The proposed method is benchmarked with the existing method. Effects of frequency, daytime and night time, height of air layer, and conductivity of air layer and ionosphere on EM fields are discussed.
